QuantScenarioBench/qsb-heston

QuantScenarioBench — Heston Benchmark Dataset

This dataset is a representative benchmark sample generated by QuantScenarioBench, a JAX-native framework for reproducible stochastic market scenario generation.

It contains 10,000 independent simulation paths under the Heston stochastic volatility model over 252 daily time steps (1 year horizon). Each path includes both the asset price trajectory (observation) and the instantaneous variance trajectory (latent state).

Need a larger or custom dataset? This file is a fixed benchmark sample. To generate datasets at any scale — more paths, different parameters, non-uniform time grids, or other market models — use the QuantScenarioBench library directly:

pip install quantscenariobench

See the GitHub project for full documentation and examples.

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Model Description

The Heston model (Heston, 1993) extends Black-Scholes by making the instantaneous variance $v_t$ itself a stochastic process. The asset price and variance evolve jointly:

$$d{S}_t=\mu S_{t}dt+\sqrt{v_t}{S}_{t}d{W}_t^{S}dS\_t\; =\; \backslash mu\backslash ,S\_t\backslash ,dt\; +\; \backslash sqrt\{v\_t\}\backslash ,S\_t\backslash ,dW^S\_t$$ $$d{v}_t=\kappa (\theta -v_t)dt+\xi \sqrt{v_t}d{W}_t^v,\text{Corr}(d{W}_t^S,d{W}_t^v)=\rho dv\_t\; =\; \backslash kappa(\backslash theta\; -\; v\_t)\backslash ,dt\; +\; \backslash xi\backslash ,\backslash sqrt\{v\_t\}\backslash ,dW^v\_t,\; \backslash quad\; \backslash text\{Corr\}(dW^S\_t,\; dW^v\_t)\; =\; \backslash rho$$

Key properties:

• Stochastic volatility — variance fluctuates around its long-run mean $\theta$ and reverts at speed $\kappa$
• Leverage effect — negative $\rho$ correlates downward price moves with rising volatility (realistic for equities)
• Feller condition — $2\kappa\theta \geq \xi^2$ ensures the variance process stays strictly positive

Parameters used for this dataset

Parameter	Value	Description
S0	100.0	Initial asset price
mu	0.0	Drift (risk-neutral; $r = 0$)
kappa	2.0	Variance mean-reversion speed (half-life ≈ 4 months)
theta	0.04	Long-run variance ($= 20%$ vol)
xi	0.3	Vol-of-vol
rho	−0.7	Asset–variance correlation (leverage effect)
v0	0.04	Initial variance ($= 20%$ vol)

Feller condition satisfied: $2 \times 2.0 \times 0.04 = 0.16 \geq 0.3^2 = 0.09$.

The risk-neutral setting (mu=0) and identical initial vol (v0=theta=0.04) to the Black-Scholes benchmark make ATM option prices directly comparable across models.

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Simulation Configuration

Field	Value
Time grid	linspace(0.0, 1.0, 253) — 252 daily steps over 1 year
Number of paths	10,000
PRNG seed	42
Backend	JAX CPU (float64)
Library version	1.0.0
Dataset version	1.0.0

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Column Schema

All QuantScenarioBench datasets share the same 12-column schema regardless of the market model used. This enables direct cross-model comparison by loading datasets with identical code.

Column	Type	Description
observation	list<float64>	Asset price path $S_{t_0}, \ldots, S_{t_T}$; one row per path
latent_state	list<float64>	Instantaneous variance path $v_{t_0}, \ldots, v_{t_T}$; same length as observation
seed	int64	Integer PRNG seed used to reproduce this batch
prng_key_info	string	JAX PRNGKey derivation description
model_name	string	Heston
model_version	string	Model specification version
parameters	string	JSON-encoded model parameters
time_grid	string	JSON-encoded array of 253 time points
n_paths	int64	10000
library_version	string	quantscenariobench library version
dataset_version	string	Dataset version identifier (independent of library version)
generated_at	string	UTC ISO-8601 generation timestamp

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Usage

from datasets import load_dataset
import numpy as np

ds = load_dataset("QuantScenarioBench/qsb-heston", split="train")

# Each row is one simulated path
row = ds[0]
prices    = np.array(row["observation"])    # shape (253,) — asset price
variances = np.array(row["latent_state"])   # shape (253,) — instantaneous variance
vols      = np.sqrt(variances)              # instantaneous vol
print(f"S0={prices[0]:.2f}  S_T={prices[-1]:.2f}  avg_vol={vols.mean():.3f}")

# Stack all paths
all_prices = np.stack([ds[i]["observation"]  for i in range(len(ds))])
all_vars   = np.stack([ds[i]["latent_state"] for i in range(len(ds))])
print(all_prices.shape)  # (10000, 253)
print(all_vars.shape)    # (10000, 253)

Cross-model comparison

All three benchmark datasets share the same schema and time grid:

bs  = load_dataset("QuantScenarioBench/qsb-black-scholes",  split="train")
h   = load_dataset("QuantScenarioBench/qsb-heston",          split="train")
rb  = load_dataset("QuantScenarioBench/qsb-rough-bergomi",   split="train")

import numpy as np
for name, ds in [("BS", bs), ("Heston", h), ("rBergomi", rb)]:
    terminals = np.array([ds[i]["observation"][-1] for i in range(len(ds))])
    print(f"{name:10s}  mean={terminals.mean():.2f}  std={terminals.std():.2f}")

Generate a custom dataset

from quantscenariobench.api import simulate
from quantscenariobench.export import export_parquet, publish_to_hub
from quantscenariobench.interface import TimeGrid
from quantscenariobench.models import Heston
import jax.numpy as jnp

model    = Heston(mu=0.0, kappa=1.5, theta=0.06, xi=0.4, rho=-0.8, v0=0.06, S0=100.0)
tg       = TimeGrid(jnp.linspace(0.0, 2.0, 505))   # 2-year horizon
scenario = simulate(model, tg, n_paths=100_000, seed=99)

export_parquet([scenario], "my_heston_dataset.parquet")
# or: publish_to_hub([scenario], "my-org/my-heston-dataset")

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Reproducibility

Simulation paths are bit-identical across runs on the same computational backend when using the same seed, library_version, and model parameters.

Cross-backend bit-identity is not guaranteed. JAX floating-point operations may produce different bit patterns across hardware backends (CPU, GPU, TPU) even with identical inputs. The seed, prng_key_info, and library_version columns document full provenance so that any differences can be traced to backend changes rather than parameter or code drift.

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Related Datasets

Model	Dataset
Black-Scholes	QuantScenarioBench/qsb-black-scholes
Heston (this dataset)	QuantScenarioBench/qsb-heston
Rough Bergomi	QuantScenarioBench/qsb-rough-bergomi

All three datasets use the same time grid, seed, and initial spot for direct cross-model comparison.

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Citation

If you use this dataset or QuantScenarioBench in your research, please cite the GitHub repository.